Problem #NZO-000003

Problem

Let $A B C D$ be a square and let $X$ be any point on side $B C$ between $B$ and $C$ . Let $Y$ be the point on line $C D$ such that $B X = Y D$ and $D$ is between $C$ and $Y$ . Prove that the midpoint of $X Y$ lies on diagonal $B D$ .

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